What is the derivative of 6x^2ln(6x) ?

The derivative of 6x^2ln(6x) is 6(2xln(6x)+x)

What is the first derivative of 6x^2ln(6x) ?

The first derivative of 6x^2ln(6x) is 6(2xln(6x)+x)

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derivative of

6 x^{2} ln (6 x)

6 (2 x ln (6 x) + x)

Solution steps

\frac{d}{d x} (6 x^{2} ln (6 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (x^{2} ln (6 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = ln (6 x)

= 6 (\frac{d}{d x} (x^{2}) ln (6 x) + \frac{d}{d x} (ln (6 x)) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

= 6 (2 x ln (6 x) + \frac{1}{x} x^{2})

\frac{1}{x} x^{2} = x

= 6 (2 x ln (6 x) + x)

2^{(x^{2} - 3 x + 8)}

f (x) = 5 + 8 x, at x = 0

x \to \infty lim (x \cdot \frac{1}{x})

\frac{1}{120 x}

\int_{- 2}^{2} f (x) d x

What is the derivative of 6x^2ln(6x) ?
The derivative of 6x^2ln(6x) is 6(2xln(6x)+x)
What is the first derivative of 6x^2ln(6x) ?
The first derivative of 6x^2ln(6x) is 6(2xln(6x)+x)